1、Advanced SynopticM.D.EastinBaroclinic Instability Basic Idea Simple Models Classic Eady Framework Contributions from Barotropic Instability Examples of Observational EvidenceBaroclinic InstabilityAdvanced SynopticM.D.EastinDefinition Spontaneous growth of a small-scale perturbations within a basic-s
2、tate environment Energy source for the growth is drawn from the basic-state environmentDifferent Types of“Instability”Convective instability Convective clouds grow as parcels tap into the background CAPE Kelvin-Helmholtz instability Wave-like clouds grow (and“break”)as parcels tap into the backgroun
3、d vertical shearConcept of InstabilityAdvanced SynopticM.D.EastinDefinition Spontaneous growth of a small-scale perturbations within a basic-state environment Energy source for the growth is drawn from the basic-state environmentDifferent Types of“Instability”Barotropic instability Disturbances grow
4、 by extracting kinetic energy from the background flow suction-vortices in tornadoes meso-vortices in hurricanes short-waves in jet stream Baroclinic instability Disturbances grow by extracting potential energy from the background flow Synoptic-scale wavesConcept of InstabilityAdvanced SynopticM.D.E
5、astinQuestions:QG theory and polar-front theory have taught us that the development and intensification of a surface cyclone requires the interaction of the fledgling surface cyclone or stationary front with a pre-existing upper-level wave.What mechanism develops the upper-level waves?What determine
6、s the size,structure,and intensity of the upper-level waves?What basic-state conditions are required for the waves to develop?Our Approach:Your text(Chapter 7)provides a very well-written and thorough explanation of baroclinic instability via the classic theoretical framework first presented by Eady
7、(1949)This will be(has been)presented in detail in Advanced Dynamics Here,we will address the relevant results from a practical perspectiveBaroclinic InstabilityAdvanced SynopticM.D.EastinReview of Potential and Kinetic Energy:Baroclinic Instability“Available”Potential EnergyNo kinetic energyUnstabl
8、e Situation“Growth”of Wileys fall speed due to extraction of potential energy from the basic-state environment(conversion of potential energy to kinetic energy)Advanced SynopticM.D.EastinThe Basic Idea:“Coin Model”Consider a coin resting on its edge (an“unstable”situation)Its center of gravity(or ma
9、ss)is located some distance(h)above the surface As long as h 0,the coin has some “available potential energy”If the coin is given a small push to one side,it will fall over and come to rest on its side (a“stable”situation)The instability was“released”and“removed”Its center of gravity was lowered and
10、 thus its potential energy was decreased The coins motion represents kinetic energy that was converted from the available potential energyBaroclinic InstabilityCenter ofGravityhh 0Advanced SynopticM.D.EastinThe Basic Idea:“Simple Atmosphere”Consider a stratified four-layer atmosphere with the most d
11、ense air near the surface at the pole and the least dense near the tropopause above the equator (an“unstable”situation)Each layer has a center of gravity()located some distance above the surface Each layer has some available potential energy The entire atmosphere also has a center of gravity()and so
12、me available potential energy If the atmosphere is given a small“push”(e.g.a weak cyclone)then the layers will move until they have adjusted their centers of gravity to the configuration that provides lowest possible center of gravity for the atmosphere(the most“stable”situation)The baroclinic insta
13、bility was released and removed Each layers motion represents a portion of the total atmospheric kinetic energy that was converted from the atmospheres available potential energyBaroclinic InstabilityTPEquatorPoleSurfaceTropopauseLightHeavyEquatorPoleLightHeavyAdvanced SynopticM.D.EastinThe Basic Id
14、ea:“Simple Atmosphere”Several“events”occurred during this process in our simple atmosphere that are commonly observed in the real atmosphere:Kinetic energy(or wind)was generated similar to the increase in winds as a weak low pressure system intensifies Warm(less dense)air was lifted over cold(more d
15、ense)air in a manner very similar to fronts There is a poleward transport of warm air and an equatorward transport of cold air similar to the typical temperature advection pattern around a low pressure system.Baroclinic InstabilityTPEquatorPoleSurfaceTropopauseLightHeavyEquatorPoleLightHeavyAdvanced
16、 SynopticM.D.EastinEady Framework:Energy Conversion Processes Basic-state environment consists of a strong north-south temperature gradient with an upper-level zonal jet stream(atmosphere in thermal wind balance)Basic-state environment contains both available potential energy and kinetic energy Inst
17、ability is initiated by(1)perturbation flow inducing weak localized WAA and CAA across the thermal gradient warm and cold air parcels(or eddy potential energy)Eddy kinetic energy is then generated(2)as warm parcels rise and cold parcels sink Acceleration of initial parcels away from their origin cre
18、ates(via mass continuity)more WAA and CAA or creates more eddy potential energy(3)Baroclinic Instability123System continues to intensify(increase its eddy kinetic energy)until is can no longer generateeddy potential energy(becomes a closed occluded system)Advanced SynopticM.D.EastinEady Framework:Id
19、ealized Situation Maximum growth rate occurs for waves with wavelengths of 3000-6000 km Synoptic scale Maximum growth rate occurs for waves tilting west with height(21 phase shift)Greater tilt no intensification Less tilt no intensification We look for westward tilt Stacked systems are mature Eddy k
20、inetic energy develops from an upward heat flux Warm air rising poleward Cold air sinking equatorward Similar to warm/cold frontsBaroclinic InstabilityLHLHTroughRidgeNortherliesSoutherliesWarmColdAdvanced SynopticM.D.EastinProduction of Eddy Kinetic Energy Our analysis of baroclinic instability show
21、ed that the synoptic waves/cyclones are essentially systems of eddy kinetic energy What else can create eddy kinetic energy?Term A:Eddy Kinetic Energy(EKE)ProductionTerm B:Baroclinic Generation Upward heat flux produces EKE Warm air rising/cold air sinkingTerm C:Barotropic Generation Function of loc
22、ation relative to zonal mean jet stream Function of mean momentum flux Lets examine a few scenariosContributions from Barotropic InstabilityyuvuTgpRvuDtDgggdgg222Term ATerm BTerm CSee your text(Section 2.7)For full derivationAdvanced SynopticM.D.EastinBarotropic Production of Eddy Kinetic Energy:Ter
23、m C:Perfectly Circular EddyContributions from Barotropic InstabilityyuvuTgpRvuDtDgggdgg222Term ATerm BTerm CAverage of ugvg over entire eddyis zeroCircular systemsdo NOT intensifyfrom barotropicprocesses(but they can from)(baroclinic processes)Advanced SynopticM.D.EastinBarotropic Production of Eddy
24、 Kinetic Energy:Term C:Asymmetric Eddy with Negative TiltContributions from Barotropic InstabilityyuvuTgpRvuDtDgggdgg222Term ATerm BTerm CAverage of ugvg over entire eddyis negative“Negatively tilted”systemsCAN intensifyfrom barotropicprocesses IF located south of the u maximumAdvanced SynopticM.D.E
25、astinBarotropic Production of Eddy Kinetic Energy:Contributions from Barotropic Instabilityt=0t=0t=0t=+6 hrsAdvanced SynopticM.D.EastinObservational Evidence for Possible Cyclogenesis?Answer#1:When a jet core is upstream of a trough axis that is above and west of a weak surface low Upstream jet stre
26、aks have large positive vorticity on their poleward flank with PVA downstream near the trough axis and over the weak surface low PVA ascent Psfc decreases P increases EKE increases enhances WAA/CAA maintains any ongoing baroclinic instability processBaroclinic/Barotropic InstabilityExample of a Trou
27、gh with an Upstream Jet StreakL+Advanced SynopticM.D.EastinObservational Evidence for Possible Cyclogenesis?Answer#2:When a diffluent trough is above and west of a weak surface low Diffluent upper-level troughs induce deep-layer ascent Ascent Psfc decreases P increases EKE increases enhances WAA/CAA
28、 maintains any ongoing baroclinic instability processBaroclinic/Barotropic InstabilityNote how the distancebetween the 6 heightcontours increasesdownstream of thetrough axis Example of a Diffluent TroughLAdvanced SynopticM.D.EastinObservational Evidence for Possible Cyclogenesis?Answer#3:When a nega
29、tively-tilted trough is above and west of a weak surface low and south of the zonal mean jet core Negative tilts permit barotropic processes to generate a net increase in eddy kinetic energy EKE enhances WAA/CAA maintains any ongoing baroclinic instability processBaroclinic/Barotropic InstabilityExa
30、mple of a Negatively-tilted TroughLNote how the slopeof the trough axisis negative in theX-Y coordinatesystemXYAdvanced SynopticM.D.EastinObservational Analysis Tips:Not all negatively-tilted troughs intensify Not all diffluent troughs intensify Not all troughs with upstream jet cores intensify Must
31、 evaluate the vertical tilt of the system Westward may intensify(21 optimal)Stacked should not intensify much Eastward should not intensify Must evaluate the latitude of the zonal mean jet core Negatively-tilted systems south of the jet core may intensify Positively-tilted systems north of the jet c
32、ore may intensify Negatively-tilted systems north of the jet core should not intensify Positively-tilted systems south of the jet core should not intensify Should evaluate all forcing terms in modified QG Omega equation Should evaluate all forcing terms in modified QG Height Tendency equation Barocl
33、inic/Barotropic InstabilityAdvanced SynopticM.D.EastinReferencesBluestein,H.B,1993:Synoptic-Dynamic Meteorology in Midlatitudes.Volume II:Observations and Theory of WeatherSystems.Oxford University Press,New York,594 pp.Bretherton,F.P.,1966:Critical layer instability in baroclinic flows,Quart.J.Roy.
34、Meteor.Soc.,92,325-334.Charney,J.G.,1947:the dynamics of long waves in a baroclinic westerly current.J.Meteor.,6,56-60.Eady,E.T.,1949:Long waves and cyclone waves.Tellus,1,33-52.Lackmann,G.,2019:Mid-latitude Synoptic Meteorology Dynamics,Analysis and Forecasting,AMS,343 pp.Orlanski,I.,1968;Instability of frontal waves.J.Atmos.Sci.,25,178-200.谢谢你的阅读v知识就是财富v丰富你的人生谢谢！
